It is known in the art relating to two stroke engines of the type having cylinder exhaust ports to provide a cooling jacket to cool the upper portions of the engine cylinders above the ports where the cylinders are exposed to combustion gas temperatures. It is also known from U.S. Pat. No. 4,736,716 Ohyama to provide additional cooling for the engine piston through passages extending below the side exhaust and end transfer ports of an engine. These passages apparently do not extend below the side inlet ports opposite the exhaust ports but connect with a circumferential jacket portion above the ports.